An acoustic bandgap (ABG) is the phononic analog of a photonic bandgap (PBG), wherein a range of acoustic frequencies are forbidden to exist in a structured material. ABGs are realized by embedding periodic scatterers in a host matrix that propagates an acoustic wave. The scatterer material has a density and/or elastic constant that is different than that of the matrix material, leading to destructive interference of the acoustic wave when the lattice constant of the phononic crystal structure is comparable to the wavelength of the acoustic wave. If the interference is destructive, the energy of the acoustic wave is reflected back and the wave cannot propagate through the phononic crystal. This destructive interference creates the ABG. In principle, the bandgap can be created at any frequency or wavelength simply by changing the size of the unit cell of the crystal. The spectral width of the ABG is directly related to the ratio of the densities and sound velocities in the different materials comprising the structure. In general, the larger the ratio, the wider the bandgap. For example, the bandwidth of an ABG-based acoustic isolator, Δω, can exceed 0.5 ωg, where ωg is the center (midgap) frequency of the ABG. See M. M. Sigalas and E. N. Economou, J. Appl. Phys. 75, 2845 (1994). This wide bandwidth distinguishes ABG acoustic isolators from previously developed one-dimensional quarter-wave acoustic reflectors. Further, for two- or three-dimensional phononic crystals, the frequency and width of the bandgap will depend on the direction of propagation.
Most of the prior ABG work has been limited to large, hand-assembled structures at frequencies below 1 MHz (i.e, structures with lattice constants of order one millimeter or greater), where the ABG matrix material was either water or epoxy. See T. Miyashita, Meas. Sci. Technol. 16, R47 (2005). Investigation of higher frequency ABCs in solid low-loss materials has recently been reported for surface acoustic wave (SAW) devices where ABCs have been demonstrated at 200 MHz by etching air hole scatterers in lithium niobate and silicon. See S. Benchabane et al., Proc. of SPIE 6128, 61281A-1 (2006); and T. Wu et al., “J. Appl. Phys. 97, 094916 (2005).
However, there remains a need for bulk wave acoustic bandgap (BAW ABG) devices fabricated using microelectromechanical systems (MEMS) technologies. Such microfabricated BAW ABG devices would be useful for acoustic isolation of devices operating in the ultrasonic, VHF, or UHF regime (i.e., frequencies of order 1 MHz to 10 GHz and higher, and lattice constants of 100 μm or less), such as radio frequency (rf) resonators and gyros. By defecting the acoustic bandgap device through removal or modification of the scatterers, microscale phononic elements, such as waveguides, couplers, high-Q cavities, filters, mirrors, and lenses, can be realized, enabling phononic integrated circuits and impacting fields such as communications, ultrasound, and non-destructive testing. Further, microscale BAW devices have several significant advantages over SAW approaches. In SAW devices, energy can leak into the substrate, introducing loss in cavities and waveguides. Conversely, BAW ABG devices can be placed in vacuum and acoustically isolated from the substrate, completely confining the acoustic energy inside a two-dimensional ABG device. Other advantages of the microfabricated BAW ABG devices are small size and compatibility with conventional complementary-metal-oxide-semiconductor (CMOS) fabrication processes.